Parameters

All the parameters in the current version of the model are listed in Table 3.

Table 3. Sources for the base values in parentheses: 1: (D'Agata et al., 2005) , 2: (Sørensen et al., 2001), 3:

(Webb et al., 2005), 4: (D'Agata et al., 2007), 5: (Doebbeling et al., 1992).

Parameter Function Type/range Base value

Days How many days the simulation is run Integer -

Number of rooms Number of rooms in the hospital Integer 80 (1)

Room capacity Number of patients in a single room Integer 5 (1)

Mean DOS + StdDev Mean duration of stay and standard deviation Integer 5 (1) ± 1 Initial infection

probability

The probability that an incoming patient is S infected 0…1 0.07 (4)

HCW amount Amount of health care workers in the hospital Integer 100 (1) Hourly room visit (base) Number of rooms visits/hr assuming activity of 1.0 >= 0 3 Hand washing compliance Probability that an HCW washes hands 0…1 0.4 (5) Hand washing frequency The frequency of hand washing events list After contact HCW activity (hourly) Defines actual visits/hr by multiplying the base value 0…1 See Figure 7 Contact probability Probability of HCW contacting a patient when in a

room

0…1 0.207 (1)

Contamination probability Probability of HCW contamination in contact 0…1 0.4 (1) Colonization probability Probability of patient infection in contact 0…1 0.06 (1) Max load Maximum bacterial load (K in logistic growth eq.) Double 1.1x10¹¹ (3) Infection threshold Threshold for patient being infectious Double 10¹¹ (1,2) Standard rd Default intrinsic growth factor, when no effectors

(competition or medicine) present

> 0 0.413

Antibiotic rd add The effect of antibiotics on S bacteria’s rd < 0 -0.5 (3) Phage therapy rd add The effect of PT on RA bacteria’s rd < 0 -0.5

Inoculant Amount of bacteria upon infection > 0 10⁶ (2)

Non-treatment tag add Universal rd when patient is tagged non-treated < 0 -0.03 S comp. factor Superiority of S against other bacteria, when

antibiotics are not present (i.e tradeoff from resistance)

<= 0 -0.2905 (3,4)

Universal comp. factor Superiority of resistant bacteria, when under selective pressure

>= 0 -0.2905 (3,4)

Conjugation constant Change of growth rates due to HGT from RA to S >= 0 0.1 RA ground probability Probability of spontaneous emergence of RA in healthy

patient Treatment threshold The point of the infection cycle when medicine may be

described

Double 10¹¹

Probability of treatment The probability of the doctor prescribing medicine 0…1 1.0

Simultaneous treatment Whether antibiotics and PT are used simultaneously Boolean - RA seed The date for initial RA infection. Overrides regular

mutation mechanisms.

day 150

RP seed The date for initial RP infection. Overrides regular mutation mechanisms.

day 200

The base values shown in Table 3 are the standard values used in the forthcoming experiments, unless otherwise stated. The values are derived from a handful of studies representing different hospital settings. The bacteria are assumed to be types of species, which live on the skin, respiratory tracts or digestive systems of humans as described in Lipsitch et al. (2000). The proportion of incoming patients already infected with S varies greatly from study to study. The value of 0.07 estimated by D'Agata et al. (2007) was compatibility with the logistic growth equation. For practical purposes, the software also calculates and displays the doubling time using the formula !"  (!)

!" !!!" (D'Agata et al., 2006).

Rd is then approximated to be 0.413 for susceptible bacteria (before treatments) to provide a doubling time of two hours as shown by Webb et al. (2005).

The superiority of S bacteria against other bacteria under no medicine simulates the tradeoffs brought about by resistance (Table 2). This advantage in fitness remains even while under antibiotic treatment, but since antibiotics efficiently eradicate S bacteria, the less-fit strains are not affected for long – as soon as S bacteria disappear, the rd of RA and RP bounce back to their original value (unless medication or competition between RA and RP have effects). The baseline competition values (the S competition factor is set to -0.2905) provide a doubling time of approximately six hours for RA/RP bacteria under no

medication (D'Agata et al., 2007; Webb et al., 2005). More complex fitness-relationships may be explored in future versions of the model.

The conjugation cofactor (base value 0.1, estimate) simulates HGT between resistant and non-resistant bacteria. This transforms S bacteria to the RA class, speeding up the growth of RA and decaying the S population. The model approximates the maximum load 1.1 * 10¹¹ (the logistic growth equation requires the maximum load to be larger than the infection threshold, hence the factor 1.1). Antibiotics reduce rd of S bacteria by 0.4, leading to an rd of -0.05. For PT the reduction is assumed similar. In practice, this causes a fully saturated patient to be cleared of the bacterium in approximately in ten days (Webb et al., 2005).

Resistant bacteria may emerge in a patient through spontaneous infection or through vector (HCW) mediated transfer. The former is defined by the parameter ‘RA

ground probability’ for patient with no infection and by ‘S to RA mutation prob.’ for patient already colonized with S. Again, the mutational parameters refer to patients being fully saturated with the original strain. The mutation probabilities between different bacterial types are based on estimates. One of the goals of this study is to explore the parameter space for interesting combinations of mutational probabilities.

The treatment threshold currently equals the infection threshold, since this is the point when the doctors are assumed to notice infections and prescribe treatment. The timing of treatment hour is not arbitrary – it strongly affects global infection dynamics.

The later the event is set, the more time the patient has to spread the pathogens via HCWs.

This is aspect is discussed in detail later.

The amount of interaction between HCWs and patients is usually represented by contact rate per patient (per unit time). Previously, the rate was determined to be 8-10 contacts per patient in a day, depending on the infection status of the patient (D'Agata et al., 2005). Due to the object-oriented simulation approach implemented in this model, the contact rate cannot be explicitly inserted as a parameter. However, transformation between the two types of systems is straightforward. The contact rate per person (/day) can be

The base values in Table 3 are calibrated so that the contact rate settles around 9 – the average value used by Agata et al. (2005). The software automatically calculates the rate and displays it in the data section of the graphical user interface, so implementation of parameters derived from previously published studies is easier.

HCWs are not assumed to be uniformly active throughout the day. Figure 7 shows a proposed model of HCW-activity. This model has no backing data and is simply an estimate. The activity factor multiplies the “hourly room visit” –parameter. This is then used to obtain the actual number of room visits per hour for each HCW. The activity table in Figure 7 is used as the base value for all forthcoming experiments.

Figure 7. An approximation of HCW-activity through a single day. X-axis shows the hour of day. The activity on the Y-axis is the factor determining the number of room visits in an hour.